| William Enfield - Astronomy - 1832 - 282 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, **is to their difference, as the tangent of half the sum of the angles at the** baseRSM, RMS, is to the tangent of half their difference. Tohalfthe sum add half the difference, and... | |
| John Radford Young - Astronomy - 1833 - 308 pages
...tan. i (A + B) a — b ~ "tan. i ( A — B j ' that is to say., in any plane triangle the sum of any **two sides is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. By help of this rule we may determine the... | |
| Euclides - 1834 - 518 pages
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in **to their difference, as the tangent of half the sum of the** angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at... | |
| Euclid - 1835 - 540 pages
...half the difference, and it will give the less. PROP. III. FIG. 8. In a plane triangle, the sum of any **two sides is to their difference, as the tangent of half the sum of the angles at the base,** to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides AB,... | |
| Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides **is to their difference, as the tangent of half the sum of the angles at the base** to the tangent of half their difference. * PROP. IV. F1G. 8. In a plane triangle, the cosine ofhalftke... | |
| Adrien Marie Legendre - Geometry - 1836 - 382 pages
...b + c=2p; we have a + 6 — c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal **triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles** opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem... | |
| John Playfair - Geometry - 1836 - 148 pages
...triangle, any three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any **two sides is to their difference, as the tangent of half the sum of the angles at the base,** to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides, AB,... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle **is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...sine of a right angle is equal to the radius. PROP. III. THEOR. THE sum of any two sides of a triangle **is to their difference, as the tangent of half the sum of the angles** opposite to those sides, is to the tangent of half their difference. Let ABC be a triangle, a, b any... | |
| Charles Davies - Navigation - 1837 - 342 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, **is to their difference, as the tangent of half the sum of the** two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
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